Average Error: 11.3 → 1.3
Time: 5.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r575162 = x;
        double r575163 = y;
        double r575164 = z;
        double r575165 = t;
        double r575166 = r575164 - r575165;
        double r575167 = r575163 * r575166;
        double r575168 = a;
        double r575169 = r575168 - r575165;
        double r575170 = r575167 / r575169;
        double r575171 = r575162 + r575170;
        return r575171;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r575172 = x;
        double r575173 = y;
        double r575174 = a;
        double r575175 = t;
        double r575176 = r575174 - r575175;
        double r575177 = z;
        double r575178 = r575177 - r575175;
        double r575179 = r575176 / r575178;
        double r575180 = r575173 / r575179;
        double r575181 = r575172 + r575180;
        return r575181;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original11.3
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.3

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
  2. Using strategy rm

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]

  4. Final simplification1.3

    \[\leadsto x + \frac{y}{\frac{a - t}{z - t}}\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))